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Inspired by the method of null dimensional reduction and by the holographic correspondence between Vasiliev's higher-spin gravity and the critical O(N) model, a bulk dual of the unitary and the ideal non-relativistic Fermi gases is proposed.
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Although the null reduction is tricky in gravity, a promising route is to follow: C. Duval, G. Burdet, H. P. Kunzle and M. Perrin, Phys. Rev. D 31
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This result is a corollary of the following general results on 𝔰 𝔭 ( 2 d , ℝ ) \mathfrak{sp}(2d,\mathbb{R}) -covariant unfolded equations: M. A. Vasiliev, Phys. Rev. D 66
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Non-relativistic kinematical symmetries are symmetry transformations, ψ ( t , 𝐱 ) → γ ( g ( t , 𝐱 ) ) ψ ( g − 1 ( t , 𝐱 ) ) \psi(t,{\bf x})\to\gamma\big(g(t,{\bf x})\big)\,\psi\big(g^{-1}(t,{\bf x})\big) , thus its generators are first-order differential operators
Cited in the paper.
D. T. Son, Phys. Rev. D 78
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C. Duval, M. Hassaine, P. A. Horvathy, Annals Phys. 324
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The general structure of such non-relativistic higher-spin conserved currents was found in: O. A. Gelfond and M. A. Vasiliev, JHEP 0903
2009
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W. D. Goldberger, JHEP 0903
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X. Bekaert, E. Joung and J. Mourad, JHEP 1102
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M. Valenzuela, [arXiv:0912.0789 [hep-th]]
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X. Bekaert, E. Meunier and S. Moroz, arXiv:1111.3656 [hep-th]
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